Departamento de Ingeniería Electrónica

This work addresses the task of a mobile sensor platform searching for a moving target. We show that minimizing the entropy of the probability distribution of the target state estimate can result in a control input for the mobile sensor that acquires the target in less iterations than an exhaustive search. We also show that this approach can be used to track the target after it is acquired. We apply a particle filter framework to estimate the state of the target and propose an informationbased cost function to optimize as part of a control law for the mobile sensor. We include simulation results to illustrate the performance of our approach.

In this paper, we address the design of an optimally unbiased moving average (MA) filter for time error online estimating and synchronization in Global Positioning System (GPS)-based timekeeping. We proceed from the slowly changing nature of a time error generated by a local clock, assuming its function to be linear for N points in the average. Employing the inherent property of a simple MA to produce the lowest noise for the given averaging interval and using linear regression as a proper stochastic approximation to evaluate the bias, we find the optimal weighting coefficients. The designed optimally unbiased MA filter and its improved modification produce two times more noise than a simple MA when N 1. Both the numerical simulation and the filtering of the real GPS-based time error processes are provided and discussed in detail.

The paper addresses a new unbiased p-step toward predictive finite impulse response (FIR) filter for a class of discrete-time deterministic state space models, which states are represented on a horizon of N past points with degree polynomials and observed independently. It is implied that measurements are not available at a current time point n. The problem arises in synchronization and tracking when a signal is lost. Generic coefficients are derived via the Bernoulli polynomials for a two-parameter family of the polynomial filter gains. A generalization is provided for the linear (ramp) and quadratic filter gains. We show that the solution proposed is efficient in applications to predictive filtering of the states of local clocks of digital communication network nodes when a synchronizing signal is temporarily not available.

In this paper, we find the optimal horizons and sampling intervals, both in the sense of the minimum mean square error (MSE), for a one-parameter family of the discrete-time unbiased finite impulse response (FIR) filters. On a horizon of N l points in the nearest past, the FIR and the model k-state are represented with the l-degree and m-degree polynomials, respectively. The noisefree state space model is observed in the presence of zero-mean noise of an arbitrary distribution and covariance. The approach is based on the following. The FIR filter produces an unbiased estimate if l m. In order to reduce the noise, N l needs to be increased. The model fits the increased horizon with a higher degree polynomial, m > l. Minimization of the mean square error for m > l gives the optimal horizon and sampling interval. Justification is provided for the global positioning system (GPS)-based measurements of the first state of a local crystal clock provided in the presence of uniformly distributed sawtooth noise induced by the GPS timing receiver.

We address an unbiased finite impulse response (FIR) filter for discrete-time state-space models with polynomial representation of the states. The unique -degree polynomial FIR filter gain and the estimate variance are found for a general case. The noise power gain (NG) is derived for white Gaussian noises in the model and in the measurement. The filter does not involve any knowledge about noise in the algorithm. It is unstable at short horizons, 2 , and inefficient (NG exceeds unity) in the narrow range , where is ascertained by the cross-components in the measurement matrix C. With , the filter NG poorly depends on C and fits the asymptotic function ( + 1) 2 . With very large 1, the estimate noise becomes negligible and the filter thus optimal in the sense of zero bias and zero noise. Having such properties, the proposed unbiased FIR filter fits well slowly changing with time models. An example is given for a two-state system.

In this paper, we present an optimal finiteimpulse response (FIR) filter for the linear time-interval error (TIE) model of a local clock and compare its estimates to those obtained by the unbiased FIR filter via the global positioning system (GPS)-based sawtooth measurements. We show theoretically and verify experimentally that there is no reasonable necessity in using optimal filters for GPSbased estimation of the TIE of precision crystal, rubidium, and cesium clocks. For these clocks, the optimal FIR filter requiring four coefficients degenerates to a simple unbiased FIR filter requiring only one coefficient.

This paper addresses a statistical analysis of the limiting estimate errors of the time delay (phase difference) between two reflectors of the passive wireless surface acoustic wave (SAW) sensor with single differential measurement. The estimation is provided in a sense of the maximum likelihood function at the ideal coherent receiver in the presence of Gaussian noise. Assuming the Gauss-shape interrogating radio frequency pulse, we prove that linear drifts in its amplitude and phase do not affect the distribution of the sensor phase (and phase difference) at the measurement point. Rigorous and approximate solutions for the mean and mean-square errors, along with the error probability for the estimate to exceed a threshold, are studied in detail. The plots are applied to evaluate the errors in a wide range of signal-to-noise ratios and thresholds. Practical recommendations for designers of the remote SAW sensor interrogating systems are also given.

The von Mises/Tikhonov probability density function (pdf) is examined to use as an approximation for the differential phase in presence of Gaussian noise in systems with differential phase measurement (DPM). It is shown that this approximation is the best fit for the phase difference between two vectors with equal signal-to-noise ratios (SNRs). The strategy is proposed to derive the approximate pdf for the case of infinite SNR in one of the vectors. Two approximating pdfs are derived for the differential phase diversity with different and equal SNRs. An application is given for the error probability in passive wireless remote SAW sensing with DPM. r

A new trend in self-contained (without the use of quantum discriminators) frequency stabilization of an oven controlled crystal oscillator (OCXO) and frequency standard is proposed and discussed. The method developing the trend is called a modulational method and is based on the use of the reference properties of crystal resonator natural bulk vibrations (double-frequency and multi-frequency oscillators are not used in this case). The concept is based on dynamic modulation characteristics of an oscillator, and basic relationships are found for their calculation. The construction principles of the frequency control systems are formulated substantiating mathematically the essence of the method. Basic ratios of modulating signals are determined, the solution of which shows only a slight influence of the modulation signal on the Allan variance and spectral density of an OCXO. The results of the method's practical use are considered. Their subject is the OCXO with the oven system adapted to the ambient temperature and crystal frequency standard with aging rate compensation.